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Course Search Results

  • MATH 311: Abstract Algebra I

    3.00 Credits
    Kutztown University of Pennsylvania

    Sets, relations, and functions; groups; rings; integral domains; fields; elementary theory of groups.
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  • MATH 312: Abstract Algebra II

    3.00 Credits
    Kutztown University of Pennsylvania

    Extension of Abstract Algebra I topics; permutation groups; normal sub-groups and quotient groups; rings and ideals; ring homomorphisms; quotient rings, integral domains and their fields of quotients; fields; polynomial rings.
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  • MATH 321: Combinatorics

    3.00 Credits
    Kutztown University of Pennsylvania

    This is an introductory course in combinatorics. Topics include introductory and advanced counting techniques, graph theory, and selected topics chosen from recurrence relations, generating functions and integer partitions, and extremal combinatorics.
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  • MATH 325: Applied Time Series Analysis

    3.00 Credits
    Kutztown University of Pennsylvania

    This course presents the fundamental knowledge of time series analysis for both theory and applications. Topics include exploratory data analysis tools, methods for detrending, and seasonal adjustment of data, smoothing techniques such as exponential smoothing, modeling and forecasting based on the ARIMA models. Examples will be drawn from a variety of disciplines including business, finance, economics, and biology. Statistical packages will be used for data analysis.
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  • MATH 327: Design and Analysis of Experiments

    3.00 Credits
    Kutztown University of Pennsylvania

    This course presents proper design and analysis of experiments, including completely randomized designs, designs with factorial treatment structure, random and mixed effects, complete and incomplete blocked designs, Latin Squares, confounding, split plots, fractional factorials, and response surfaces. Examples from a broad range of subject areas will be presented.
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  • MATH 330: Theory Of Numbers

    3.00 Credits
    Kutztown University of Pennsylvania

    This is an introductory course in number theory. The topics covered begin with divisibility and factorization, the Fundamental Theorem of Arithmetic, prime numbers, greatest common divisor, and least common multiples. The course continues with congruences and arithmetic functions. The remainder of the course introduces one or more advanced topics such as quadratic residues, primitive roots, Diophantine equations, continued fractions, and cryptography.
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  • MATH 332: Numerical Analysis

    3.00 Credits
    Kutztown University of Pennsylvania

    Numerical methods fundamental to scientific computing are developed. Topics include finite difference calculus; zeros of a function; matrix computations; solutions to systems of linear equations; approximation by polynomials; numerical differentiation and integration; numerical solutions of ordinary differential equations; rounding errors and other types of errors. Selected algorithms will be run on the computer. Students will be required to use appropriate computer software.
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  • MATH 337: Introduction to Cryptography

    3.00 Credits
    Kutztown University of Pennsylvania

    The course is an introduction to cryptography, the study of securing communication and information. This course will cover the mathematical, algorithmic, and historical aspects of classical and modern cryptography. We will also introduce students to personal encryption software as well as programming libraries and computer algebra systems that allow one to perform large computations necessary for cryptographic applications. Topics will include classical and modern symmetric ciphers, public-key cryptography (e.g. RSA), various cryptographic protocols, and any other topics of interest to the instructor and students. All necessary theoretical background will be reviewed, but some background in number theory, abstract algebra, probability, or computer science will be expected.
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  • MATH 340: Differential Equations

    3.00 Credits
    Kutztown University of Pennsylvania

    In this course students will develop an understanding of the basic theory, applications and connections of linear algebra and differential equations. Topics include: first, second, and higher order ordinary differential equations; methods of solutions include exact, substitution reduction, undetermined coefficients, variation of parameters, power series solutions, the Laplace Transform, and system of linear differential equations. Consideration is given to applications to the physical and natural sciences. Students will be required to use appropriate computer software.
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  • MATH 347: Introduction to Dynamical Systems

    3.00 Credits
    Kutztown University of Pennsylvania

    This course is meant to provide an introduction to nonlinear dynamics and chaos theory. An emphasis will be placed on qualitative analysis for both continuous and discrete dynamical systems. Key concepts will include fixed/ equilibrium points and periodic solutions, linear stability analysis and asymptotic behavior, bifurcation analysis for parameterized families, and existence of periodic orbits. The latter part of the course will focus on chaos theory with topics including period-doubling bifurcations, strange attractors, and Lyapunov exponents. Classic and real-world models will be stressed. Throughout the course, programming in scientific computing software (e.g. MATLAB) will be introduced and reinforced.
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